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4
USAMO 2002 Problem 4
USAMO 2002 Problem 4
Source:
September 30, 2005
functional equation
USAMO
Problem Statement
Let
R
\mathbb{R}
R
be the set of real numbers. Determine all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
2
−
y
2
)
=
x
f
(
x
)
−
y
f
(
y
)
f(x^2 - y^2) = x f(x) - y f(y)
f
(
x
2
−
y
2
)
=
x
f
(
x
)
−
y
f
(
y
)
for all pairs of real numbers
x
x
x
and
y
y
y
.
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